中文摘要：

基于超声速细长体运动理论，采用理想可压缩流体无旋定常流动以及超空泡尾部 Riabushinsky 闭合方式假定，建立了描述水下超声速条件下细长锥型射弹超空泡流动的非线性积分-微分方程。针对超声速流动特点，发展了该方程数值离散和迭代求解的新方法，采用一阶近似解作为超空泡流动数值计算的初始解，优化了初始迭代条件，提高了计算速度和精度。通过与超空泡细长比渐近解结果进行比较，验证了理论模型和计算方法的正确性及有效性。在超声速条件下，分析了流体压缩性效应以及不同马赫数对细长锥型射弹超空泡形态、表面压力系数和压差阻力系数的影响，为超空泡射弹的弹型优化和水中弹道预报提供了理论基础。

英文摘要：

On the assumption that the ideal compressible fluid motion is irrotational and steady,super-cavitating closure with the Riabushinsky scheme,and based on the slender body theory at supersonic speed,a nonlinear integro-differential equation for the supercavitating flow around a slender cone type projectile traveling in water at supersonic speed was derived.According to the features of supersonic flow,the new numerical discrete and iteration methods solving the equation were developed.By tak-ing the first order approximation solution as initial value of numerical calculation to supercavitating flow,the iteration condition was optimized,and the calculated speed and precision were improved.By comparing the computed results with the asymptotic solutions provided by the foreign literature about the slenderness ratio of supercavitation,the correctness and validity of the theoretical model and cal-culation method were verified.At supersonic speed,the compressibility effects of fluid were taken in-to account,and the supercavitation profile,surface pressure coefficient and pressure drag coefficient of the slender cone type projectile at different Mach numbers were analyzed.The research provided the theoretical basis for the shape optimization and underwater ballistic forecast of supercavitating proj ec-tile.